document.write( "Question 924353: Given P(A|B) = .7 , and P(B|A) = .6 , which is larger, P(A) or P(B)? Show work . \n" ); document.write( "
Algebra.Com's Answer #560786 by Theo(13342)\"\" \"About 
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p(a|b) = p(ab) / p(b)\r
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\n" ); document.write( "\n" ); document.write( "p(b|a) = p(ab) / p(a)\r
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\n" ); document.write( "\n" ); document.write( "you know what p(a|b) is and you know what p(b|a) is.\r
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\n" ); document.write( "\n" ); document.write( "you also know that p(ab) is the same in either equation.\r
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\n" ); document.write( "\n" ); document.write( "let x = p(ab) and replace p(a|b) with .7 and replace p(b|a) with .6 and you get:\r
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\n" ); document.write( "\n" ); document.write( ".7 = x/p(b)\r
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\n" ); document.write( "\n" ); document.write( ".6 = x/p(a)\r
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\n" ); document.write( "\n" ); document.write( "solve for p(b) in the first equation to get p(b) = x/.7\r
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\n" ); document.write( "\n" ); document.write( "solve for p(a) in the second equation to get p(a) = x/.6\r
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\n" ); document.write( "\n" ); document.write( "since x/.6 is bigger than x/.7, p(a) must be bigger.\r
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